Every square matrix can be associated with a real number called its determinant.
You can refer to the determinant of matrix
The determinant of the matix above is given by
The determinant of a triangular matrix is given by the product of the elements on its main diagonal.
A triangular matrix can be:
Upper triangular: All 0's below the main diagonal.
Lower triangular: All 0's above the main diagonal.
Diagonal matrix: All 0's except for the main diagonal.
The minor
The cofactor is given by:
That means that the cofactors and the minors differ by just a sign(at most). The sign depends on the position of the entry.
The determinant of a square matrix is the sum of the entries in the 1st row multiplied by their cofactors.
I think we can do this with any row or column of the matrix.
Usually we take the row/column with the most 0's.
If
If you don't feel like doing the thing with cofactors, you can try to turn the matrix into a triangular one, taking into consideration how the determinant changes when we apply elementary row operations.
You can also use these opeations to create more zeros in a row or column, as to make the cofactor process easier.
If
If
A square matrix
If
If
If
If
The transpose of this matrix is called the adjoint of